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Mathematical construction defines oscillation characteristics in linear differential equations, indicating potential applications in diverse fields.
For any finite set of nonnegative numbers containing zero, we construct a linear homogeneous differential equation of a given order $$>2$$ with continuous coefficients on the nonnegative half-line whose spectra of characteristic frequencies and strong oscillation exponents of signs, zeros, and roots coincide with this set.
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Artisevich et al. (2025) studied this question.
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